Weird Al’s Keen Eye

By Matt, on August 28th, 2010

If you follow “Weird Al” Yankovic on Twitter (and really, why wouldn’t you?), you may have noticed this picture, which he posted earlier this week along with the tweet “Wow, waffles for just .25 cents? That means I can get 400 for a dollar!!”

Kudos to you, Mr. Yankovic, for spotting what I can only assume to be a mathematical error of the type we’ve seen before. If this music thing doesn’t pan out, maybe you can work for Verizon.

Then again, maybe it’s not an error, in which case I can only hope that Weird Al wastes no time in naming this establishment, so that I can patronize it before they catch wise.

This criticism really annoys me. The use of a lower-case roman letter “c” with a vertical stroke through it to indicate cents is a convention. Likewise, the use of a period (“.”) to indicate the decimal position in a string of digits is also a convention. (Indeed, in parts of the world, people conventionally use other symbols, such as a comma, to indicate this decimal position.) AND, conventionally, by most people apart from those of us trained in mathematics, the use of the two symbols together in the one expression — the decimal period and the cents letter c-with-a-stroke — means the same as the use of the c-with-a-stroke symbol does by itself. Their use together does NOT mean, conventionally, what your criticism suggests it does (1/400th of a dollar in the case of “0.25c”).

Of course, the conventional meaning of these two symbols is not compositional, to use a technical term from the theory of semantics (in linguistics, or logic, or the theory of computer programme languages). In other words, we can’t infer the meaning of the two symbols combined from knowing the meaning of each one separately. However inconsistent or possibly undesirable, non-compositionality does not make the conventional interpretation invalid.

http://www.mathgoespop.com Matt

Hi Peter, thanks for your comment. I agree with you, of course – I don’t think anyone would misinterpret this sign as saying that each waffle is only a fraction of a cent, nor would I argue on the side of a customer who demanded that price based on the sign. I’m pretty sure that Weird Al intended this as a joke, as do I.

On the other hand, this disparity between conventions (writing cents as .25, for example, vs. .25 cents) does lead to important differences in cases where fractions of cents occur (for example, data plans in cell phone contracts). The 100 fold difference between .25 dollars and .25 cents has let to customer frustration on more than one occasion (here’s one example, but there are others too). In other words, I do believe there are situations when this distinction does make an important difference, and furthermore, I also know there are people who (unfortunately) do not understand this difference. So, to the extent that I can highlight this difference (even through a joke, as this post attempts to do), I think it certainly does no harm to get people thinking about it. Again, in a case such as this, I think one can unambiguously identify what the price of the waffle is – but when we replace waffles with other things, that may no longer be the case.

Anyway, I appreciate your feedback – certainly I don’t want to come across as curmudgeonly, and I do realize that trying to seriously argue that these waffles cost a fraction of a cent is ridiculous.